On the possibility of using the Galerkin projection method to model the spatial distribution of minority charge carriers generated by an electron probe in a semiconductor

In this paper, the results of using the Galerkin projection method to model the spatial distribution of minority charge carriers generated by an electron probe in a semiconductor material are presented. The problem is solved in the cylindrical coordinate system. The sought distribution is found in the form of the partial sum of the double Fourier series using the system of modified Laguerre functions. An order estimate of the residual error corresponding to approximate solution of the steady-state equation of their diffusion is given. The approximate calculated results are compared with the exact solution of the one-dimensional equation.